This article is one professor's mix of opinion and elementary introduction to the concept of conjecture, and IMO is quite rambling and inconsistent. Why are yo

This article is one professor's mix of opinion and elementary introduction to the concept of conjecture, and IMO is quite rambling and inconsistent. Why are you generalizing this one random person's thoughts into a conclusion about mathematics as a discipline? Don't let one poor thinker (or perhaps merely poor writer) spoil it for you. The author seems to have completely missed the actual reason we find conjectures interesting: we're asking ourselves, "do we have the techniques to prove this kind of problem?" That's the fundamental reason disproving a conjecture is less celebrated than proving it, because disproving is often done by finding a single counterexample, which doesn't teach us much about our proof techniques -- unless, of course, the process of finding that counterexample was particularly new and interesting! The most interesting question to ponder with a conjecture is not "is this true?", but rather "why is this hard to prove?". The most boring answer to the latter is "oh, because it's false", while the most exciting answer is "because we were missing this fundamental idea that can spawn an entire new branch of mathematics." It's all about the journey, not the destination.